Beautiful graphic of the types of contempt (courtesy Haley Martin): https://www.instagram.com/p/CGserHlDad3/
The narcissist and psychopath have contempt for: weakness; perceived inferiority (moral, intellectual) and this contempt often masquerades as altruism and sanctimonious self-righteousness; for inadequacy: win-lose zero sum failure, loser; emotions (especially on display); vulnerability; neediness, clinging; attachment/bonding/love; empathy; altruism;
The narcissist inflicts pain and abuse on others. He devalues Sources of Supply, callously and off-handedly abandons them, and discards people, places, partnerships, and friendships unhesitatingly. Some narcissists - though by no means the majority - actually ENJOY abusing, taunting, tormenting, and freakishly controlling others ("gaslighting"). But most of them do these things absentmindedly, automatically, and, often, even without good reason.
What is unusual about the narcissist's sadistic behaviours - premeditated acts of tormenting others while enjoying their anguished reactions - is that they are goal orientated. "Pure" sadists have no goal in mind except the pursuit of pleasure - pain as an art form (remember the Marquis de Sade?). The narcissist, on the other hand, haunts and hunts his victims for a reason - he wants them to reflect his inner state. It is all part of a mechanism called "Projective Identification".
When the narcissist is angry, unhappy, disappointed, injured, or hurt - he feels unable to express his emotions sincerely and openly since to do so would be to admit his frailty, his neediness, and his weaknesses. He deplores his own humanity - his emotions, his vulnerability, his susceptibility, his gullibility, his inadequacies, and his failures. So, he makes use of other people to express his pain and his frustration, his pent up anger and his aggression. He achieves this by mentally torturing other people to the point of madness, by driving them to violence, by reducing them to scar tissue in search of outlet, closure, and, sometimes, revenge. He forces people to lose their own character traits - and adopt his own instead. In reaction to his constant and well-targeted abuse, they become abusive, vengeful, ruthless, lacking empathy, obsessed, and aggressive. They mirror him faithfully and thus relieve him of the need to express himself directly.
Having constructed this writhing hall of human mirrors, the narcissist withdraws.